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The study of a ratio-dependent predator-prey model with stage structure in the prey. (English) Zbl 1183.92083

Summary: A ratio-dependent predator-prey model with stage structure in the prey is constructed and investigated. In the first part of this paper, some sufficient conditions for the existence and stability of three equilibriums are obtained. In the second part, we consider the effect of impulsive release of predator on the original system. A sufficient condition for the global asymptotical stability of the prey-eradication periodic solution is obtained. We also obtain a condition, under which the prey would never be eradicated, i.e., the impulsive system is permanent. At last, we give a brief discussion.

MSC:

92D40 Ecology
34A37 Ordinary differential equations with impulses
34D20 Stability of solutions to ordinary differential equations
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